Z. H. Li

Prediction of the first spinning cylinder test using continuum damage mechanics

For many years large-scale experiments have been performed world-wide to validate aspects of fracture mechanics methodology. Special emphasis has been given to correlations between small- and large-scale specimen behaviour in quantifying the structural behaviour of pressure vessels, piping and closures. Within this context, the first three spinning cylinder tests, performed by AEA Technology at its Risley Laboratory, addressed the phenomenon of stable crack growth by ductile tearing in contained yield and conditions simulating pressurized thermal shock loading in a PWR reactor pressure vessel. A notable feature of the test data was that the effective resistance to crack growth, as measured in terms of the J R-curve, was appreciably greater than that anticipated from small-scale testing, both at initiation and after small amounts (a few millimetres) of tearing. In the present paper, two independent finite element analyses of the first-spinning cylinder test (SC 1) are presented and compared. Both involved application of the Rousselier ductile damage theory in an attempt to understand better the transferability of test data from small specimens to structural validation tests. In each instance, the parameters associated with the theorys constitutive equation were calibrated in terms of data from notched-tensile and (or) fracture mechanics tests, metallographic observations and (or) chemical composition. The evolution of ductile damage local to the crack tip during SC 1 was thereby calculated and, together with a crack growth criterion based on the maximisation of opening-mode stress, used as the basis for predicting cylinder R-curves (angular velocity vs. Δa, J integral vs. Δa). Except in the initiation region, the results show the Rousselier model to be capable of predicting correctly the enhancement of tearing toughness of the cylinder relative to that of conventional test specimens, given an appropriate choice of finite element cell size in the region representing the crack tip. As such, they represent a positive step towards achieving the goal to establish continuum damage mechanics as a reliable predictive engineering tool.

Some experience in the use of damage mechanics to simulate crack behaviour in specimens and structures

Damage mechanics offers the possibility of representing the failure of components directly, without the use of characterising parameters such as the K or J of fracture mechanics. It does so by allowing the material to develop damage and fail at the level of the continuum mechanics description. Within the regime of ductile fracture, the method tries to encapsulate the loss of strength associated with void growth around the most significant second phase particles. Figure 1 illustrates diagramatically the process of void growth and the encapsulation of it in a ‘cell’ which represents at the continuum level the complex mechanics evolving within it as the cell softens and fails. Damage mechanics models these complex processes by building into the material constitutive equations the terms that represent the cell softening. The technique has been used successfully at SheffieldI to predict some of the spinning cylinder tests performed at AEA Risley.3 Figures 2 and 3 show the damage mechanics predictions for cylinders 1 and 3 in comparison with the experimental data and that from laboratory compact specimens. The enhancement of tearing resistance in the cylinders is correctly predicted directly from the computer simulation.

Three-dimensional damage theory of crack growth in large centre-cracked panels using the element removal technique

Abstract The conventional use of continuum ductile damage mechanics in finite element analysis identifies the crack tip or crack front by some criterion which, on the basis of developing parameters, deems a certain region to be cracked. In the region deemed to be cracked there is thus only a reduction in stresses, which thereafter falls continually. This paper incorporates in the damage model for both two and three dimensions, a facility which enables elements to be ‘switched off’ ehind the predicted crack front so that the stresses there are zero. A three-dimensional finite element analysis using this element removal scheme is performed to predict the deformation of centre-cracked panels under uniaxial and equibiaxial loading and to study the applicability of this scheme.

The use of constraint-modified failure assessment lines in failure assessment diagrams

Two possible methods of including the effect of constraint in a failure assessment diagram (FAD) of the R6 type are to change the definition of the quantity Kr(the ratio of the operative crack driving force to the current material toughness) or to modify the failure assessment line (FAL). An analysis of the relation between the treatment of ductile tearing using the FAD and the R-curve diagram, extended recently to include constraint effects in modified diagrams of the first type is shown here also to hold for the second. Provided that the projected growth path image (PGPI) is used to specify the motion of the assessment point during crack growth there is a complete correspondence of R-curve analysis with either type of FAD. The two methods, both formulated for any number of generic constraint parameters, are compared using a simple illustrative example in which the constraint is parametrized by T. The methods previously discussed for testing the consistency or conservatism of an engineering FAD can be extended to both types of generalized diagram which allow for crack tip constraint.